Stochastic Modeling and Simulation in the Design of Multicenter Clinical Trials
Frank Mannino1
Richard Heiberger2
Valerii Fedorov1
1Research Statistics Unit, GlaxoSmithKline2Department of Statistics, Temple University
Outline
• Motivation for using modeling & simulation in designing late-stage clinical trials
• Simulation approach used at GSK• Example using RExcel interface• Conclusions
Issues in Multicenter Clinical Trials
• Late stage clinical trials are costly and inefficient– Simplistic assumptions lead to underpowered trial– Variability not properly accounted for– Drug supply process can be very wasteful
• Independent design decisions are made about interacting factors
Interacting Design Factors
• Patient recruitment– How many centers, how long will we wait, etc.
• Randomization• Statistical modeling
– How many patients, best analysis model, etc• Patient dropouts• Drug supply
Use of Simulations
• Emphasizing only a single design factor can sometimes permit analytic results– e.g., finding sample size
• Dealing with multiple interacting factors (or abnormal design characteristics) cannot be handled analytically
• Simulations allow us to handle interactions
R Package
• Multicenter Simulation Toolkit (MSTpackage)– Developed within Research Statistics Unit at GSK– Has been used for approximately 15 different
studies• Typical run of 10,000 simulations will take
between a 1 and 6 hours, depending on complexity and number of scenarios being considered
Highlights: Recruitment & Randomization
• Patients simulated according to Poisson process– Rates for each center sampled from a Gamma
distribution• Randomization includes permuted block,
biased coin, & minimization– Stratification by center, region, previous
treatment, or other covariates
RExcel Interface
• RExcel is an add-in that allows the full functionality of R to be accessed from Excel
• Allows sharing of complex R-based programs with users who have no knowledge of R
• Communication between the programs is hidden from the user
Toolkit interface
Interactions between R & Excel
Drug Supply
• Once virtual patients are recruited and randomized, we can apply various drug supply strategies– e.g., when & how much drug to ship both to
centers and regional depots– Allows us to chose a scenario that minimizes cost
while also controlling for the number of patients without drug
Drug Supply
Outputs of Interest
• Statistical power• Length of trial• Cost of trial• Drug supply considerations
– Probability of patients being without drug
Important to consider variability in these output values!
Length of Recruitment & Trial
Length of recruitment
4 5 6 7
0.0
0.2
0.4
0.6
0.8
1.0
Length of trial
5 6 7 8 9
0.0
0.2
0.4
0.6
0.8
1.0
Patient Loss as a Function of Overage
0 20 40 60 80 100
0.0
0.2
0.4
0.6
0.8
1.0
Overage
Pro
babi
lity
of X
or
less
pat
ient
s w
ithou
t dr
ug
# of patients without drug
0124816
60% probability of 0 patients without drug
95% probability of 8 or less patients without drug
95% probability of 0 patients without drug
Overage = Percent excess drug supply
Decisions & Information Gained with MST Toolkit
• Choice of randomization– Whether to stratify by center
• Distribution of costs• Waiting times for recruitment and trial
completion• Imbalances between treatment arms• More realistic estimate of power of study
Conclusions
• Modeling & Monte Carlo simulation is the best way to understand the interactions between various design factors– All outcomes (power, costs, etc.) are distributions
• Using better designs will lead to more statistically robust results and more cost efficient designs
• The RExcel interface increases the impact of the R software within GSK
References
• Anisimov, V. and Fedorov V., “Modeling, prediction and adaptive adjustment of recruitment in multicentre trials”, Stat in Med., 26: 4958–4975
• Thomas Baier and Erich Neuwirth (2007), Excel :: COM :: R, Computational Statistics 22/1, pp. 91-108
• R Development Core Team (2010). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.